Magnification determines image size as actual size times magnification factor

Steps:

• Convert actual diameter to meters: 0.5 μm = 0.5 × 10^{-6} m = 5 × 10^{-7} m.
• Express magnification in scientific notation: ×50,000 = 5 × 10^4.
• Calculate image diameter: 5 × 10^{-7} m × 5 × 10^4 = 25 × 10^{-3} m = 2.5 × 10^{-2} m.

Why C is correct:

• Magnification formula states image size = actual size × magnification, directly yielding 2.5 × 10^{-2} m for option C.

Why the others are wrong:

• A: Underestimates by factor of 10 due to unit conversion error.
• B: Underestimates by factor of 10 in magnification application.
• D: Overestimates by factor of 10 in final calculation.

Final answer: C